This disclosure relates generally to color formulation and more particularly to generating a color formula for matching a bi-directional color.
Bi-directional colors, unlike typical diffuse colors, appear to change color as the angle of illumination and observation changes. Examples of bi-directional colors include metallic colors, pearlescent colors, and interference colors. Bi-directional colors have been used for decades in small volumes by the paint and cosmetic industry. More recently, bi-directional colors are beginning to spread to new mainstream applications in the plastic, paint, textile, ink, and cosmetic industries.
To achieve a bi-directional color, usually a flake, disk or platelet-shaped pigment ingredient is used in the material's formula. These platelet-shaped pigments typically have particle diameters that are sufficiently large (10 to 100 microns) with a relatively smooth surface, yet are relatively thin (0.1 to 1 microns). Light that hits one of these platelet-shaped pigment particles, can either undergo specular mirror like reflection as in the case of metallic flake pigments or can be partially transmitted and undergo interference as in the case of interference or pearlescent pigments. For both of these cases, the platelet-shaped pigment particles do not scatter the light in a diffuse way like typical spherical, cubical, or low aspect ratio irregularly shaped pigment particles. Because the platelet-shaped particle does not scatter the light in a diffuse manner, it maintains its bi-directional nature. Another property of the platelet-shaped pigment particle is its ability to align with flow during mixing and processing due to its high aspect ratio. This partial or full alignment can significantly change the angle dependence of the physical color.
When color matching bi-directional colors, the industry has had to rely on trial and error methods and artistic expertise because of the lack of computational methods and measurement tools. Typically, a color technician is given a physical sample of the target bi-directional color to match. They measure the target color using a spectrophotometer to get a color measurement. With this measurement, the technician uses standard diffuse color matching tools and methods, such as described in U.S. Pat. No. 5,668,633, entitled Method and System for Formulating a Color Match, to get a diffuse color formula. This diffuse color formula is composed of pigments and dyes of various concentrations that when mixed and compounded together in a material generate a physical color that is diffuse. The technician would then use this diffuse color formula as a starting point and begin a trial-and-error process. First the technician would produce a trial batch using the starting point formula and evaluate how well it matched the physical target color under all angles of observation and illumination. To improve the match under the various angles, the technician would use their own expertise to decide what concentrations of platelet-shaped pigment particles to add in order to better match the bi-directional color. They would then produce another trial batch and once again evaluate how well it matched the physical target color under all angles of observation and illumination. This iterative process would proceed until either a match was achieved or the technician gave up. The industry calls this process “matching the color flop.”
The problem with this trial-and-error approach is that it is very slow and relies on the presence of a very experienced color technician who can evaluate a color under multiple angles and decide on how best to modify the color formula. Because the number of application of bi-directional colors is increasing, there is now the need for an efficient systematic computational approach that can generate a color formula composed of pigments and dyes that matches a bi-directional color under all angles of observation and illumination.